Theorem ee121

Description: e121 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee121.1	$$⊢\phi \to \psi$$
	ee121.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
	ee121.3	$$⊢\phi \to \tau$$
	ee121.4	$$⊢\psi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee121	$$⊢\phi \to \left(\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee121.1	$$⊢\phi \to \psi$$
2		ee121.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3		ee121.3	$$⊢\phi \to \tau$$
4		ee121.4	$$⊢\psi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	a1d	$$⊢\phi \to \left(\chi \to \psi \right)$$
6	3	a1d	$$⊢\phi \to \left(\chi \to \tau \right)$$
7	5 2 6 4	ee222	$$⊢\phi \to \left(\chi \to \eta \right)$$